A key feature of a quantum foam is its non-local nature. While non-locality is undesirable in quantum field theory, the situation in quantum gravity is open.
It is often said that the only way to cure the divergences appearing
perturbatively in quantizations of gravity without introducing new physics (i.e., string theory or super-symmetric extensions of gravity), is to introduce some kind of non-locality in the action which smears out Green functions evaluated on
one point only. Until now, ghosts in the theory have blocked research in this direction (some progress has been
achieved recently in [1]}).
For the purposes of the present work, it is important to note that there are two possible types of non-locality which contribute in different ways. One,
violation of microlocality, disappears when the cut-off is taken to zero, while the other, violation of macrolocality, or disordered locality, does not [2]}. Violations of macrolocality amount to the presence of
what a relativist would call a wormhole [3]}, a path through spacetime disallowed in a Lorentzian topology.
General relativity allows for such paths and, in principle, they should be taken into account in a full quantum theory of gravity. In principle, in order to have traversable
wormholes, the common positive-energy conditions and some other conditions on the throats have to be satisfied.
